Question

How was the presumed age of the Universe determined?

Answer 1

Using Hubble's law.

Explanation:

Hubble's law states that the further away a galaxy is, the faster it is moving:

`v prop d`

Because of this law, if it is extrapolated backward, it is implied that everything in the universe was once concentrated at one point- supporting the idea of the big bang and also makes it possible to estimate how long ago it was when everything was in one place- i.e the birth of the universe.

However, this is not using SI units, but rather the units for velocity is `kms^-1` and distance is measured in Mega-parsecs `MPc`.

This equation, being linear must have a constant- Hubble's constant:

`H_o`

Making the equation:

`v=H_od`

The value of the constant varies throughout the universe but on a VERY rough estimate we can say that the value of the constant is :

`H_o=70 kms^-1 MPc^-1`

This constant allows us to estimate the age of the universe using the equation:

`1/H_o approx T`

However, the Hubble constant must be transferred into SI units for this to work...

So let's find the value of the constant:
`70 kms^-1=70 000 ms^-1`

1 parsec= 3.26 ly= `3.08 times 10^16 m`

1 Mega-parsec(1 million parsecs)=`(3.08 times 10^16 times 10^6m)`

`H_o=70 kms^-1 MPc^-1=(70 times 10^3)/(10^6 times 3.08 times 10^16)= 2.27 times 10^-18`

Inverse it to find Hubble time:

`1/(2.27 times 10^-18) approx T`

`T approx 4.4 times 10^17 s`

`T approx 1.4 times 10^10` years

Which is almost 14 billion years, but scientists often say that the value is 13.8 with an uncertainty of `+-0.2` billion years, so we are within the acceptable range.

And that is basically how the age of the universe can be estimated.